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Biometrika 1993 80(1):27-38; doi:10.1093/biomet/80.1.27
© 1993 by Biometrika Trust
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Bias reduction of maximum likelihood estimates

DAVID FIRTH

Department of Mathematics, University of Southampton SO9 5NH, U.K.

It is shown how, in regular parametric problems, the first-order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function. In exponential families with canonical parameterization the effect is to penalize the likelihood by the Jeffreys invariant prior. In binomial logistic models, Poisson log linear models and certain other generalized linear models, the Jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data.

Key Words: Asymptotic bias; • Biased estimating equations; • Exponential family; • Generalized linear model; • Jeffreys prior; • Logistic regression; • Modified score; • Penalized likelihood; • Shrinkage


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